We show how to deform the map $\mathrm{Log}:{({\mathbb{C}}^{⁎})}^n\to {\mathbb{R}}^n$ such that the image of the complex pair of pants $P^{\circ }\subset {({\mathbb{C}}^{⁎})}^n$ is the tropical hyperplane by showing an (ambient) isotopy between $P^{\circ }\subset {({\mathbb{C}}^{⁎})}^n$ and a natural polyhedral subcomplex of the product of the two skeleta $S\times \mathrm{\Sigma }\subset \mathcal{A}\times \mathcal{C}$ of the amoeba $\mathcal{A}$ and the coamoeba $\mathcal{C}$ of $P^{\circ }$. This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.

中文翻译：

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剪裁一条裤子

我们展示如何使地图变形 $\mathrm{日志记录}：{（{\mathbb{C}}^{⁎}）}^{ñ}\to {\mathbb{[R}}^{ñ}$ 这样复杂的裤子的形象 $P^{\circ }\subset {（{\mathbb{C}}^{⁎}）}^{ñ}$ 是热带超平面，通过显示之间的（环境）同位素 $P^{\circ }\subset {（{\mathbb{C}}^{⁎}）}^{ñ}$ 和两个skeleta乘积的天然多面亚复合物 $\mathrm{小号}\times \mathrm{\Sigma }\subset \mathcal{一个}\times \mathcal{C}$ 变形虫的 $\mathcal{一个}$ 和浣熊 $\mathcal{C}$ 的 $P^{\circ }$。这为拓扑Strominger-Yau-Zaslow环形纤维的判别是余维2奠定了基础。